A non-relativistic microscopic mean field theory of finite nuclei is investigated where the nucleus is described as a collection of nucleons and delta resonances. The ground state properties of 90 Zr nucleus have been investigated at equilibrium and large amplitude compression using a realistic effective baryon-baryon Hamiltonian based on Reid Soft Core (RSC) potential. The sensitivity of the ground state properties is studied, such as binding energy, nuclear radius, radial density distribution, and single particle energies to the degree of compression. It is found that the most of increasing in the nuclear energy generated under compression is used to create the massive ∆ particles. For 90 Zr nucleus under compression at 2.5 times density of the normal nuclear density, the excited nucleons to ∆'s are increased sharply up to 14% of the total number of constituents. This result is consistent with the values extracted from relativistic heavy-ion collisions. The single particle energy levels are calculated and their behaviors under compression are examined too. A good agreement between results with effective Hamiltonian and the phenomenological shell model for the low lying single-particle spectra is obtained. A considerable reduction in compressibility for the nucleus, and softening of the equation of state with the inclusion of the ∆'s in the nuclear dynamics are suggested by the results.

The spherical Hartree-Fock approximation is applied to a no-core shell model with a realistic effective baryonbaryon interaction. The ground state properties of a heavy spherical neutron-rich doubly magic 208 Pb nucleus under compression are investigated. It is found that the nucleus becomes more bound with the occurrence of ∆ resonances.The creation of ∆ increases as the compression is continuous. There is a considerable reduction in the compressibility when the ∆ degree of freedom is activated. It is found that the ∆ particle is the basic component of the 208 Pb nucleus besides nucleons at the ground state without any compression. When the nucleus is compressed to about 4.31 times the ordinary density, the ∆ component is sharply increased to about 14.4% of all baryons in the system. It is found that there is a radial density distribution for ∆ at the ground state of 208 Pb nucleus without any compression. The single particle energy levels are calculated and their behaviors are examined under compression too. A good agreement was obtained between the results of the effective Hamiltonian and the phenomenological shell model for the low lying single-particle spectra.

The ground state properties of the spherical nucleus 40Ca have been investigated by using constrained spherical Hartree–Fock (CSHF) approximation at equilibrium and under high radial compression in a six major shells. The effective baryon-baryon interaction that includes the Δ(1236) resonance freedom degrees to calculate nuclear properties is used. The nucleon-nucleon (N-N) interaction is based on Reid soft core (RSC) potential. The results of calculations show that much of increase in the nuclear energy generated under compression is used to create the massive Δ particles. The number of Δ's can be increased to about 2.1% of constituents of nucleus when nuclear density reaches about 1.34 times of normal density. The single particle energy levels are calculated and their behavior under compression is also examined. A good agreement has been found between current calculations and phenomenological shell model for low lying single-particle spectra. The gap between shells is very clear and L-S coupling become stronger as increasing the static load on the nucleus. The results show a considerable reduction in compressibility when freedom degrees of Δ's are taken into account. It has been found that the total nuclear radial density becomes denser in the interior and less dense in the exterior region of nucleus. The surface of nucleus becomes more and more responsive to compression than outer region.

Constrained spherical Hartree-Fock (CSHF) calculations under radial compression are presented for 90 Zr in a model space consisting of nine major oscillator shells. An effective baryon-baryon interaction which includes the ∆ resonances is used. The nucleon-nucleon (N-N) interaction is Reid Soft Core (RSC) potential. The sensitivity of the results to the choice model space is examined. It is found that the nuclear system becomes more compressible when the model space is increased. The radial density and the number of ∆s are decreased by increasing model space. The results suggest that the behavior of single particle energies is independent of the model space.

Within the framework of the radially constrained spherical Hartree-Fock (CSHF) approximation, the resonance effects of delta on the properties of neutron-rich double magic spherical nucleus 132 Sn were studied. It was found that most of the increase in the nuclear energy generated under compression was used to create massive particles. For 132 Sn nucleus under compression at 3.19 times density of the normal nuclear density, the excited nucleons to s were increased sharply up to 16% of the total number of constituents. This result is consistent with the values extracted from relativistic heavy-ion collisions. The single particle energy levels were calculated and their behaviours under compression were examined. A meaningful agreement was obtained between the results with effective Hamiltonian and that with the phenomenological shell model for the low-lying single-particle spectra. The results suggest considerable reduction in compressibility for the nucleus, and softening of the equation of state with the inclusion of s in the nuclear dynamics.